Please wait a minute...

Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2020, Vol. 14 Issue (2) : 446-472     https://doi.org/10.1007/s11709-019-0605-8
RESEARCH ARTICLE
Wavelet-based iterative data enhancement for implementation in purification of modal frequency for extremely noisy ambient vibration tests in Shiraz-Iran
Hassan YOUSEFI1(), Alireza TAGHAVI KANI2, Iradj MAHMOUDZADEH KANI2, Soheil MOHAMMADI1
1. High Performance Computing Lab, School of Civil Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran
2. School of Civil Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran
Download: PDF(10795 KB)   HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract

The main purpose of the present study is to enhance high-level noisy data by a wavelet-based iterative filtering algorithm for identification of natural frequencies during ambient wind vibrational tests on a petrochemical process tower. Most of denoising methods fail to filter such noise properly. Both the signal-to-noise ratio and the peak signal-to-noise ratio are small. Multiresolution-based one-step and variational-based filtering methods fail to denoise properly with thresholds obtained by theoretical or empirical method. Due to the fact that it is impossible to completely denoise such high-level noisy data, the enhancing approach is used to improve the data quality, which is the main novelty from the application point of view here. For this iterative method, a simple computational approach is proposed to estimate the dynamic threshold values. Hence, different thresholds can be obtained for different recorded signals in one ambient test. This is in contrast to commonly used approaches recommending one global threshold estimated mainly by an empirical method. After the enhancements, modal frequencies are directly detected by the cross wavelet transform (XWT), the spectral power density and autocorrelation of wavelet coefficients. Estimated frequencies are then compared with those of an undamaged-model, simulated by the finite element method.

Keywords ambient vibration test      high level noise      iterative signal enhancement      wavelet      cross and autocorrelation of wavelets     
Corresponding Authors: Hassan YOUSEFI   
Just Accepted Date: 23 February 2020   Online First Date: 08 April 2020    Issue Date: 08 May 2020
 Cite this article:   
Hassan YOUSEFI,Alireza TAGHAVI KANI,Iradj MAHMOUDZADEH KANI, et al. Wavelet-based iterative data enhancement for implementation in purification of modal frequency for extremely noisy ambient vibration tests in Shiraz-Iran[J]. Front. Struct. Civ. Eng., 2020, 14(2): 446-472.
 URL:  
http://journal.hep.com.cn/fsce/EN/10.1007/s11709-019-0605-8
http://journal.hep.com.cn/fsce/EN/Y2020/V14/I2/446
Service
E-mail this article
E-mail Alert
RSS
Articles by authors
Hassan YOUSEFI
Alireza TAGHAVI KANI
Iradj MAHMOUDZADEH KANI
Soheil MOHAMMADI
Fig.1  Ammonium Nitrate periling tower.
Fig.2  Recording locations and directions: (a) locations of data recording; (b) recording directions “1” and “2”. (unit: mm)
Fig.3  Some examples of concrete destruction.
Fig.4  Recorded accelerations at different stations: (a) signal P21; (b) signal P31; (c) signal P51; (d) signal PP12; (e) signal P72.
Fig.5  Empirical evaluation of p values based on SNR-p curves for data P12. (a) SNR-p curve by the TV regularization; (b) SNR-p curve by the L2 regularization; (c) SNR-p curve by the Sobolev regularization.
Fig.6  Residual noise of the regularization-based denoising and corresponding energy in the wavelet space; plotted ranges are 0.02Max[ |W Ψ|2] | WΨ|2M ax [ | WΨ| 2]. (a) The residual noise obtained by the L2 regularization (by using Ω (f) L2); (b) the residual noise obtained by the Sobolev regularization (by using Ω (f)Sobolev); (c) the time-period representation in the wavelet space of the residual noise obtained by Ω (f) L2; (d) the time-period representation in the wavelet space of the residual noise obtained by Ω (f)Sobolev.
denoising method thresholding approach estimating method of the noise level
GCV soft GCV
GCVLevel soft GCV-Level
SURE hard SURE
SURELevel hard SURE-Level
SUREShrink soft SURE
Universal hard Universal
UniversalLevel hard Universal-Level
VisuShrink soft Universal
VisuShrinkLevel soft Universal-Level
Tab.1  Different denoising approaches with corresponding thresholding method and estimating noise level
Fig.7  Denoising of the P51 signal with different one-step wavelet-based denoising methods using Symlet[12] wavelet where Nd =13. (a) denoising with GCV method; (b) denoising with GCVLevel method; (c) denoising with SURE method; (d) denoising with SURELevel method; (e) denoising with SUREhrink method; (f) denoising with Universal method; (g) denoising with UniversalLevel method; (h) denoising with VisuShrink method; (i) denoising with VisuShrinkLevel method.
method P12 P51
SNR PSNR SNR PSNR
GCV 22.2179 46.72143 18.21671 32.48012
GCVLevel -33.2626 22.4117 -26.3399 4.871594
SURE -51.2787 22.2521 -1.3714 14.25517
SURELevel -51.2787 22.2521 -39.8919 3.420075
SUREShrink -51.2787 22.2521 -16.3401 8.145114
Universal -51.2787 22.2521 -4.22646 13.07922
UniversalLevel -35.1236 22.31927 -29.3122 3.756303
VisuShrink -51.2787 22.2521 -21.3869 6.866752
VisuShrinkLevel -45.376 22.26384 -32.9884 3.602981
Tab.2  Effects of denoising with different thresholding methods by the Symlet[12] and Nd =13
Fig.8  Variations of SNR against for P12 signal with different one-step wavelet-based denoising methods, where Nd=13. (a) soft and hard denoising with Symlet [12]; (b) soft and hard denoising with Db [8]; (c) soft and hard denoising with BattleLemarie[8].
method N(Db[n]) P12 P51
SNR PSNR SNR PSNR
GCV 2 –44.06220 22.50474 –3.89105 15.11722
GCV 3 –44.60310 22.51398 1.745215 18.18960
GCV 4 16.88966 41.75307 4.907001 20.27852
GCV 5 21.81810 46.31249 10.50614 25.38050
GCV 6 21.80349 46.34828 9.132639 24.06303
GCV 7 21.79715 46.28996 16.05011 30.35188
GCV 8 21.88650 46.39464 19.22092 33.40890
GCV 9 20.92899 45.53208 17.05526 31.40279
GCV 10 –47.54780 22.40617 15.57229 29.81848
GCV 11 –45.98960 22.43916 17.50372 31.65586
GCV 12 –47.04270 22.40797 15.54650 30.10663
Tab.3  Effects of denoising with the GCV method for “Db” wavelets, where Nd=13
method N(Symlet [n]) P12 P51
SNR PSNR SNR PSNR
GCV 2 –44.06220 22.50474 –3.89105 15.11722
GCV 3 –44.60310 22.51398 1.745215 18.18960
GCV 4 –29.29480 22.63941 1.328582 17.44202
GCV 5 –35.13940 22.37958 6.854628 22.08273
GCV 6 –41.13590 22.55448 16.61225 31.09798
GCV 7 20.87357 45.46648 12.50832 27.23006
GCV 8 –37.22440 22.52614 14.83558 29.36768
GCV 9 –36.51710 22.40699 14.93296 29.30645
GCV 10 –38.40640 22.47555 14.31810 28.91892
GCV 11 16.16067 41.13243 15.13602 29.70963
GCV 12 22.21790 46.72143 18.21671 32.48012
Tab.4  Effects of denoising with the GCV method for “Symlet” wavelets, where Nd=13
method N(BattleLemarie[n]) P12 P51
SNR PSNR SNR PSNR
GCV 2 –37.51220 22.48681 14.50130 29.00262
GCV 3 2.524623 28.41792 9.416154 24.65823
GCV 4 –39.45680 22.36815 20.25745 34.51602
GCV 5 –3.82456 21.44457 9.14055 24.06958
GCV 6 –39.71980 22.37107 19.59721 33.88775
GCV 7 –2.11519 20.21495 8.419222 23.10889
GCV 8 –39.93670 22.36848 20.21610 34.49167
GCV 9 –1.67073 19.56586 6.465177 21.24691
GCV 10 –40.13260 22.36773 20.53085 34.79046
GCV 11 –1.32343 19.16377 4.554586 19.54653
GCV 12 –40.3243 22.36709 19.7327 34.01635
Tab.5  Effects of denoising with the GCV method for “BattleLemarie” wavelets, where Nd=13
method Nd P12 P51
SNR PSNR SNR PSNR
GCV 1 –9.97622 23.26845 5.658332 19.27875
GCV 2 –19.0964 22.53899 –0.27328 16.60651
GCV 3 –20.6277 22.53432 12.68916 27.32417
GCV 4 –28.2157 22.42929 12.34322 26.96229
GCV 5 –31.7853 22.41064 12.2635 26.88179
GCV 6 17.47486 42.28752 12.57217 27.09593
GCV 7 22.22651 46.72911 12.61731 27.15701
GCV 8 22.22536 46.72797 16.6339 30.97174
GCV 9 22.22257 46.72528 16.63093 30.96646
GCV 10 22.22027 46.72262 18.22178 32.48961
Tab.6  Effect of decomposition levels (Nd ) with Symlet [12] wavelet
Fig.9  The iterative thresholding for P12 where Cnj=1.8, Symlet [12] and Nd=13. The last row contains final denoised signal and estimated noise.
Fig.10  The iterative thresholding for P12 where Cnj=2, Symlet [12] and Nd=13. The last row contains final denoised signal and estimated noise.
Fig.11  Determination of thresholds for Cnj for different enhanced data; SNRs and PSNRs are obtained by the iterative denoising method by the wavelet Symlet [12], Nd=13 and ten iterations. (a) SNR- Cnj for P12; (b) PSNR- Cnj for P12; (c) SNR- Cnjfor P51; (d)PSNR- Cnj for P51; (e)SNR- Cnj for P31; (f)PSNR- Cnj for P31; (g)SNR- Cnj for P72; (h)PSNR- Cnj for P72; (i)SNR- Cnj for P21; (j)PSNR- Cnj for P21.
iteration Symlet [4] Symlet [12]
SNR PSNR SNR PSNR
1 –7.55393 24.76396 –7.21248 24.65147
2 –4.92225 25.24466 –4.53529 25.20301
3 –3.10526 25.76809 –2.92566 25.62346
4 –1.62498 26.31642 –1.5398 26.14033
5 –0.1176 26.99467 –0.21442 26.7345
6 1.565725 27.89154 1.296935 27.54208
7 3.492652 29.12365 3.141206 28.69235
8 5.906256 30.92646 5.588525 30.51896
9 9.267875 33.77444 9.015204 33.3905
10 14.43995 38.5877 13.90964 38.10661
11 22.86539 46.97153 20.82031 44.92097
Tab.7  Iterative denoising of data P12 with parameters: Cnj=1.75and Nd=13
Fig.12  Iterative denoising of the signal P12 with ten iterations; both denoised signal and estimated noise are provided at each iteration (rows 1–5). The last row contains final denoised signal and estimated noise; evaluations are obtained with: Symlet[12], Cnj=1.75 and Nd=13.
Fig.13  Energy Density for remaining noise after ten iterations of the peeling algorithm where Nd=13; the energies are evaluated by the complex Morlet wavelet with parameters υb=2 and υc=1.75. Energies are presented for the range 0.02Max[ |W Ψ|2] | WΨ|2Max[ |W Ψ|2]. (a) noise of P12 in the wavelet space where Cnj=1.75; (b) noise of P51 in the wavelet space where C nj=1.90; (c) noise of P31 in the wavelet space where Cn j=1.90; (d) noise of P72 in the wavelet space where C nj=1.85; (e) noise of P21 in the wavelet space where Cn j=1.90.
Fig.14  Powers and energies of WTs of enhanced signals P21 and P31 and corresponding XWT and spectral power of XWT; plotted ranges are 0.02Max[ |W Ψ|2] | WΨ|2M ax [ | WΨ| 2] and 0.02Max[| WΨ|] |W Ψ| Max [| WΨ|]. (a) The spectral power of the enhanced data P21, evaluated by |WΨ(P21) |2 ; (b) the density of energy for the enhanced data P21, | WΨ(P 21)| 2; (c) the spectral power of the enhanced data P31, evaluated by |W Ψ(P31 )|2; (d) the density of energy of the enhanced data P31, | WΨ (P31)|2; (e) the spectral power of XWT for the enhanced data P21 and P31; (f) the density of | XWΨ| for the enhanced data P21 and P31.
Fig.15  Powers and energies of WTs of enhanced signals P21 and P51 and corresponding XWT and spectral power of XWT; plotted ranges are 0.02Max[ |W Ψ|2] | WΨ|2M ax [ | WΨ| 2] and 0.02Max[| WΨ|] |W Ψ| Max [| WΨ|]. (a) The spectral power of the enhanced data P51, evaluated by |W Ψ(P51 )|2; (b) the density of energy for the enhanced data P51, | WΨ (P51)|2; (c) the spectral power of XWT for the enhanced data P21 and P51; (d) the density of | XWΨ| for the enhanced data P21 and P51.
Fig.16  Powers and energies of WTs of enhanced signals P12 & P72 and corresponding XWT and spectral power of XWT; plotted ranges are 0.02Max[ |W Ψ|2] | WΨ|2M ax [ | WΨ| 2] and 0.02Max[| WΨ|] |W Ψ| Max [| WΨ|]. (a) The spectral power of the enhanced data P12, evaluated by |W Ψ(12)| 2;(b) the density of energy for the enhanced data P12, | WΨ (12)| 2;; (c) The spectral power of the enhanced data P72, evaluated by | WΨ (72)| 2;; (d) the density of energy for the enhanced data P72, |W Ψ(72)| 2;; (e) the spectral power of XWT for the enhanced data P12 and P72; (f) the density of | XWΨ| for the enhanced data P12 and P72.
Fig.17  Autocorrelations of wavelet coefficients of the enhanced data. (a) results for the enhanced P21; (b) results for the enhanced P31; (c) results for the enhanced P51; (d) results for the enhanced P12; (e) results for the enhanced P72.
method period (s)
0.0–0.5 0.5–1.0 1.0–1.5 1.5–2.0 2.0–2.5
the ambient
vibration test
0.12, 0.4 0.88, 0.92 1.05, 1.24, 1.29 1.59, 1.64, 1.8, 1.84 2.12, 2.16, 2.3
the FE modelling 0.1829, 0.1843, 0.20, 0.2138, 0.3139, 0.3232, 0.3954, 0.4118 1.6004, and 1.9738
Tab.8  Comparison of modal periods from the ambient vibration test and the FE model [117]
1 S W Doebling, C R Farrar, M B Prime. A summary review of vibration-based damage identification methods. Journal of Shock and Vibration, 1998, 30(2): 91–105
https://doi.org/10.1177/058310249803000201
2 S W Doebling, C R Farrar, M B Prime, D W Shevitz. Damage Identification and Health Monitoring of Structural and Mechanical Systems from Changes in Their Vibration Characteristics: A Literature Review. OSTI.GOV Technical Report LA-13070-MS ON: DE96012168; TRN: 96:003834. 1996
3 T H Le, Y Tamura. Modal identification of ambient vibration structure using frequency domain decomposition and wavelet transform. In: Proceedings of the 7th Asia-Pacific Conference on Wind Engineering. Taipei, China: APCWE, 2009
4 K K Wijesundara, C Negulescu, E Foerster, D Monfort Climent. Estimation of modal properties of structures through ambient excitation measurements using continuous wavelet transform. In: Proceedings of 15WCEE. Lisbon: SPES, 2012, 26: 15–18
5 A M Abdel-Ghaffar, R H Scanlan. Ambient vibration studies of golden gate bridge: I. Suspended structure. Journal of Engineering Mechanics, 1985, 111(4): 463–482
https://doi.org/10.1061/(ASCE)0733-9399(1985)111:4(463)
6 I Harik, D Allen, R Street, M Guo, R Graves, J Harison, M Gawry. Free and ambient vibration of Brent-Spence Bridge. Journal of Structural Engineering, 1997, 123(9): 1262–1268
https://doi.org/10.1061/(ASCE)0733-9445(1997)123:9(1262)
7 C Farrar, G James. System identification from ambient vibration measurements on a bridge. Journal of Sound and Vibration, 1997, 205(1): 1–18
https://doi.org/10.1006/jsvi.1997.0977
8 D M Siringoringo, Y Fujino. System identification of suspension bridge from ambient vibration response. Engineering Structures, 2008, 30(2): 462–477
https://doi.org/10.1016/j.engstruct.2007.03.004
9 H Sohn. A Review of Structural Health Monitoring Literature: 1996–2001. Los Alamos National Laboratory Report. 2004
10 T Kijewski, A Kareem. Wavelet transforms for system identification in civil engineering. Computer-Aided Civil and Infrastructure Engineering, 2003, 18(5): 339–355
https://doi.org/10.1111/1467-8667.t01-1-00312
11 J Lin, L Qu. Feature extraction based on Morlet wavelet and its application for mechanical fault diagnosis. Journal of Sound and Vibration, 2000, 234(1): 135–148
https://doi.org/10.1006/jsvi.2000.2864
12 K F Al-Raheem, A Roy, K P Ramachandran, D K Harrison, S Grainger. Rolling element bearing faults diagnosis based on autocorrelation of optimized: Wavelet de-noising technique. International Journal of Advanced Manufacturing Technology, 2009, 40(3–4): 393–402
https://doi.org/10.1007/s00170-007-1330-3
13 B Yan, A Miyamoto, E Brühwiler. Wavelet transform-based modal parameter identification considering uncertainty. Journal of Sound and Vibration, 2006, 291(1–2): 285–301
https://doi.org/10.1016/j.jsv.2005.06.005
14 X Jiang, H Adeli. Pseudospectra, MUSIC, and dynamic wavelet neural network for damage detection of highrise buildings. International Journal for Numerical Methods in Engineering, 2007, 71(5): 606–629
https://doi.org/10.1002/nme.1964
15 R A Osornio-Rios, J P Amezquita-Sanchez, R J Romero-Troncoso, A Garcia-Perez. MUSIC-ANN analysis for locating structural damages in a truss-type structure by means of vibrations. Computer-Aided Civil and Infrastructure Engineering, 2012, 27(9): 687–698
https://doi.org/10.1111/j.1467-8667.2012.00777.x
16 L Carassale, F Percivale. POD-based modal identification of wind-excited structures. In: Proceedings of the 12th International Conference on Wind Engineering. Cairns, 2007, 1239–1246
17 Y Tamura. Advanced Structural Wind Engineering. Tokyo: Springer, 2013, 347–376
18 M Meo, G Zumpano, X Meng, E Cosser, G Roberts, A Dodson. Measurements of dynamic properties of a medium span suspension bridge by using the wavelet transforms. Mechanical Systems and Signal Processing, 2006, 20(5): 1112–1133
https://doi.org/10.1016/j.ymssp.2004.09.008
19 J Lardies, S Gouttebroze. Identification of modal parameters using the wavelet transform. International Journal of Mechanical Sciences, 2002, 44(11): 2263–2283
https://doi.org/10.1016/S0020-7403(02)00175-3
20 X He, B Moaveni, J P Conte, A Elgamal, S F Masri. Modal identification study of Vincent Thomas bridge using simulated wind-induced ambient vibration data. Computer-Aided Civil and Infrastructure Engineering, 2008, 23(5): 373–388
https://doi.org/10.1111/j.1467-8667.2008.00544.x
21 Y C Ni, X L Lu, W S Lu. Field dynamic test and Bayesian modal identification of a special structure—The Palms Together Dagoba. Structural Control and Health Monitoring, 2016, 23(5): 838–856
https://doi.org/10.1002/stc.1816
22 F L Zhang, C E Ventura, H B Xiong, W S Lu, Y X Pan, J X Cao. Evaluation of the dynamic characteristics of a super tall building using data from ambient vibration and shake table tests by a Bayesian approach. Structural Control and Health Monitoring, 2017, 25(2): 1– 18
23 N Kang, H Kim, Sunyoung Choi & Seongwoo Jo, J S Hwang, E Yu. Performance evaluation of TMD under typhoon using system identification and inverse wind load estimation. Computer-Aided Civil and Infrastructure Engineering, 2012, 27(6): 455–473
https://doi.org/10.1111/j.1467-8667.2011.00755.x
24 H Wenzel, D Pichler. Ambient Vibration Monitoring. Vienna: John Wiley & Sons, 2005
25 J M W Brownjohn. Structural health monitoring of civil infrastructure. Philosophical Transactions of the Royal Society A, 2007, 365(1851): 589–622
https://doi.org/10.1098/rsta.2006.1925
26 X H He, X G Hua, Z Q Chen, F L Huang. EMD-based random decrement technique for modal parameter identification of an existing railway bridge. Engineering Structures, 2011, 33(4): 1348–1356
https://doi.org/10.1016/j.engstruct.2011.01.012
27 C S Huang, S L Hung, C I Lin, W C Su. A wavelet-based approach to identifying structural modal parameters from seismic response and free vibration data. Computer-Aided Civil and Infrastructure Engineering, 2005, 20(6): 408–423
https://doi.org/10.1111/j.1467-8667.2005.00406.x
28 S Ivanovic, M D Trifunac, E I Novikova, A A Gladkov, M I Todorovska. Instrumented 7-Storey Reinforced Concrete Building in Van Nuys, California: Ambient Vibration Survey Following the Damage from the 1994 Northridge Earthquake. Report No. CE 9903. 1999
29 S S Ivanovic, M D Trifunac, M I Todorovska. Ambient vibration tests of structures—A review. ISET Journal of Earthquake Technology, 2000, 37: 165–197
30 J M W Brownjohn, A De Stefano, Y L Xu, H Wenzel, A E Aktan. Vibration-based monitoring of civil infrastructure: Challenges and successes. Journal of Civil Structural Health Monitoring, 2011, 1(3–4): 79–95
https://doi.org/10.1007/s13349-011-0009-5
31 G D Roeck. The state-of-the-art of damage detection by vibration monitoring: The SIMCES experience. Structural Control and Health Monitoring, 2003, 10(2): 127–134
https://doi.org/10.1002/stc.20
32 D He, X Wang, M I Friswell, J Lin. Identification of modal parameters from noisy transient response signals. Structural Control and Health Monitoring, 2017, 24(11): 1–10
https://doi.org/10.1002/stc.2019
33 J N Juang, R S Pappa. Effects of noise on modal parameters identified by the eigensystem realization algorithm. Journal of Guidance, Control, and Dynamics, 1986, 9(3): 294–303
https://doi.org/10.2514/3.20106
34 S Dorvash, S N Pakzad. Effects of measurement noise on modal parameter identification. Smart Materials and Structures, 2012, 21(6): 065008
https://doi.org/10.1088/0964-1726/21/6/065008
35 P Li, S L J Hu, H J Li. Noise issues of modal identification using eigensystem realization algorithm. Procedia Engineering, 2011, 14: 1681–1689
https://doi.org/10.1016/j.proeng.2011.07.211
36 S Yoshitomi, I Takewaki. Noise-effect compensation method for physical-parameter system identification under stationary random input. Structural Control and Health Monitoring, 2009, 16(3): 350–373
https://doi.org/10.1002/stc.263
37 C S Huang, W C Su. Identification of modal parameters of a time invariant linear system by continuous wavelet transformation. Mechanical Systems and Signal Processing, 2007, 21(4): 1642–1664
https://doi.org/10.1016/j.ymssp.2006.07.011
38 B Yan, A Miyamoto. A comparative study of modal parameter identification based on wavelet and Hilbert-Huang transforms. Computer-Aided Civil and Infrastructure Engineering, 2006, 21(1): 9–23
https://doi.org/10.1111/j.1467-8667.2005.00413.x
39 W C Su, C S Huang, C H Chen, C Y Liu, H C Huang, Q T Le. Identifying the modal parameters of a structure from ambient vibration data via the stationary wavelet packet. Computer-Aided Civil and Infrastructure Engineering, 2014, 29(10): 738–757
https://doi.org/10.1111/mice.12115
40 W C Su, C Y Liu, C S Huang. Identification of instantaneous modal parameter of time-varying systems via a wavelet-based approach and its application. Computer-Aided Civil and Infrastructure Engineering, 2014, 29(4): 279–298
https://doi.org/10.1111/mice.12037
41 S L Chen, J J Liu, H C Lai. Wavelet analysis for identification of damping ratios and natural frequencies. Journal of Sound and Vibration, 2009, 323(1–2): 130–147
https://doi.org/10.1016/j.jsv.2009.01.029
42 T H Yi, H N Li, X Y Zhao. Noise smoothing for structural vibration test signals using an improved wavelet thresholding technique. Sensors (Basel), 2012, 12(8): 11205–11220
https://doi.org/10.3390/s120811205
43 N E Huang. Hilbert-Huang Transform and its Applications. Singapore: World Scientific, 2011, 1–26
44 A Teolis. Computational Signal Processing with Wavelets. Basel: Springer Science & Business Media, 2012
45 M Misiti, Y Misiti, G Oppenheim, J M Poggi. Wavelets and their Applications. Wiltshire: John Wiley & Sons, 2013
46 S Mallat. Wavelet Analysis & Its Applications. London: Academic Press, 1999
47 P Van Fleet. Discrete Wavelet Transformations: An Elementary Approach with Applications. New Jersey: John Wiley & Sons, 2011
48 M Jansen. Noise Reduction by Wavelet Thresholding. New York: Springer Science & Business Media, 2012
49 K P Soman. Insight into Wavelets: From Theory to Practice. New Delhi: PHI Learning Pvt. Ltd., 2010
50 X Jiang, S Mahadevan, H Adeli. Bayesian wavelet packet denoising for structural system identification. Structural Control and Health Monitoring, 2007, 14(2): 333–356
https://doi.org/10.1002/stc.161
51 R R Coifman, M V Wickerhauser. Adapted waveform “de-Noising” for medical signals and images. IEEE Engineering in Medicine and Biology Magazine, 1995, 14(5): 578–586
https://doi.org/10.1109/51.464774
52 R R Coifman, M V Wickerhauser. Experiments with adapted wavelet de-noising for medical signals and images. In: Time Frequency and Wavelets in Biomedical Signal Processing, IEEE press series in Biomedical Engineering. New York: Wiley-IEEE Press, 1998
53 L J Hadjileontiadis, S M Panas. Separation of discontinuous adventitious sounds from vesicular sounds using a wavelet-based filter. IEEE Transactions on Biomedical Engineering, 1997, 44(12): 1269–1281
https://doi.org/10.1109/10.649999
54 L J Hadjileontiadis, C N Liatsos, C C Mavrogiannis, T A Rokkas, S M Panas. Enhancement of bowel sounds by wavelet-based filtering. IEEE Transactions on Biomedical Engineering, 2000, 47(7): 876–886
https://doi.org/10.1109/10.846681
55 R Ranta, C Heinrich, V Louis-Dorr, D Wolf. Interpretation and improvement of an iterative wavelet-based denoising method. IEEE Signal Processing Letters, 2003, 10(8): 239–241
https://doi.org/10.1109/LSP.2003.814801
56 R Ranta, V Louis-Dorr, C Heinrich, D Wolf. Iterative wavelet-based denoising methods and robust outlier detection. IEEE Signal Processing Letters, 2005, 12(8): 557–560
https://doi.org/10.1109/LSP.2005.851267
57 J L Starck, A Bijaoui. Filtering and deconvolution by the wavelet transform. Signal Processing, 1994, 35(3): 195–211
https://doi.org/10.1016/0165-1684(94)90211-9
58 G Peyré. Advanced Signal, Image and Surface Processing-Numerical Tours. Université Paris-Dauphine, 2010
59 A Grinsted, J C Moore, S Jevrejeva. Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Processes in Geophysics, 2004, 11(5/6): 561–566
https://doi.org/10.5194/npg-11-561-2004
60 J Rafiee, P W Tse. Use of autocorrelation of wavelet coefficients for fault diagnosis. Mechanical Systems and Signal Processing, 2009, 23(5): 1554–1572
https://doi.org/10.1016/j.ymssp.2009.02.008
61 X Jiang, H Adeli. Wavelet packet-autocorrelation function method for traffic flow pattern analysis. Computer-Aided Civil and Infrastructure Engineering, 2004, 19(5): 324–337
https://doi.org/10.1111/j.1467-8667.2004.00360.x
62 A Bruns. Fourier-, Hilbert-and wavelet-based signal analysis: Are they really different approaches? Journal of Neuroscience Methods, 2004, 137(2): 321–332
https://doi.org/10.1016/j.jneumeth.2004.03.002
63 M Le Van Quyen, J Foucher, J P Lachaux, E Rodriguez, A Lutz, J Martinerie, F J Varela. Comparison of Hilbert transform and wavelet methods for the analysis of neuronal synchrony. Journal of Neuroscience Methods, 2001, 111(2): 83–98
https://doi.org/10.1016/S0165-0270(01)00372-7
64 C Rainieri, G Fabbrocino. Operational Modal Analysis of Civil Engineering Structures. New York: Springer, 2014
65 J M W Brownjohn. Ambient vibration studies for system identification of tall buildings. Earthquake Engineering & Structural Dynamics, 2003, 32(1): 71–95
https://doi.org/10.1002/eqe.215
66 S Mahato, M V Teja, A Chakraborty. Adaptive HHT (AHHT) based modal parameter estimation from limited measurements of an RC—framed building under multi—component earthquake excitations. Structural Control and Health Monitoring, 2015, 22(7): 984–1001
https://doi.org/10.1002/stc.1727
67 Z K Peng, P W Tse, F L Chu. An improved Hilbert–Huang transform and its application in vibration signal analysis. Journal of Sound and Vibration, 2005, 286(1–2): 187–205
https://doi.org/10.1016/j.jsv.2004.10.005
68 W X Yang. Interpretation of mechanical signals using an improved Hilbert-Huang transform. Mechanical Systems and Signal Processing, 2008, 22(5): 1061–1071
https://doi.org/10.1016/j.ymssp.2007.11.024
69 C Bao, H Hao, Z X Li, X Zhu. Time-varying system identification using a newly improved HHT algorithm. Computers & Structures, 2009, 87(23–24): 1611–1623
https://doi.org/10.1016/j.compstruc.2009.08.016
70 Z Wu, N E Huang. Ensemble empirical mode decomposition: A noise-assisted data analysis method. Advances in Data Science and Adaptive Analysis, 2009, 1(1): 1–41
https://doi.org/10.1142/S1793536909000047
71 I Daubechies, J Lu, H T Wu. Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool. Applied and Computational Harmonic Analysis, 2011, 30(2): 243–261
https://doi.org/10.1016/j.acha.2010.08.002
72 E Brevdo, H T Wu, G Thakur, N S Fuckar. Synchrosqueezing and its applications in the analysis of signals with time-varying spectrum. Proceedings of the National Academy of Sciences of the United States of America, 2011, 93: 1079–1094
73 C A Perez-Ramirez, J P Amezquita-Sanchez, H Adeli, M Valtierra-Rodriguez, D Camarena-Martinez, R J Romero-Troncoso. New methodology for modal parameters identification of smart civil structures using ambient vibrations and synchrosqueezed wavelet transform. Engineering Applications of Artificial Intelligence, 2016, 48: 1–12
https://doi.org/10.1016/j.engappai.2015.10.005
74 C Li, M Liang. Time-frequency signal analysis for gearbox fault diagnosis using a generalized synchrosqueezing transform. Mechanical Systems and Signal Processing, 2012, 26: 205–217
https://doi.org/10.1016/j.ymssp.2011.07.001
75 Z Feng, X Chen, M Liang. Iterative generalized synchrosqueezing transform for fault diagnosis of wind turbine planetary gearbox under nonstationary conditions. Mechanical Systems and Signal Processing, 2015, 52–53: 360–375
https://doi.org/10.1016/j.ymssp.2014.07.009
76 W J Staszewski. Identification of damping in MDOF systems using time-scale decomposition. Journal of Sound and Vibration, 1997, 203(2): 283–305
https://doi.org/10.1006/jsvi.1996.0864
77 P Areias, T Rabczuk, P Camanho. Finite strain fracture of 2D problems with injected anisotropic softening elements. Theoretical and Applied Fracture Mechanics, 2014, 72: 50–63
https://doi.org/10.1016/j.tafmec.2014.06.006
78 S Nanthakumar, T Lahmer, X Zhuang, G Zi, T Rabczuk. Detection of material interfaces using a regularized level set method in piezoelectric structures. Inverse Problems in Science and Engineering, 2016, 24(1): 153–176
https://doi.org/10.1080/17415977.2015.1017485
79 K M Hamdia, M Silani, X Zhuang, P He, T Rabczuk. Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions. International Journal of Fracture, 2017, 206(2): 215–227
https://doi.org/10.1007/s10704-017-0210-6
80 K M Hamdia, H Ghasemi, X Zhuang, N Alajlan, T Rabczuk. Sensitivity and uncertainty analysis for flexoelectric nanostructures. Computer Methods in Applied Mechanics and Engineering, 2018, 337: 95–109
https://doi.org/10.1016/j.cma.2018.03.016
81 N Vu-Bac, T Lahmer, X Zhuang, T Nguyen-Thoi, T Rabczuk. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 100: 19–31
https://doi.org/10.1016/j.advengsoft.2016.06.005
82 P Areias, T Rabczuk, D Dias-da-Costa. Element-wise fracture algorithm based on rotation of edges. Engineering Fracture Mechanics, 2013, 110: 113–137
https://doi.org/10.1016/j.engfracmech.2013.06.006
83 P Areias, T Rabczuk. Finite strain fracture of plates and shells with configurational forces and edge rotations. International Journal for Numerical Methods in Engineering, 2013, 94(12): 1099–1122
https://doi.org/10.1002/nme.4477
84 P Areias, M Msekh, T Rabczuk. Damage and fracture algorithm using the screened Poisson equation and local remeshing. Engineering Fracture Mechanics, 2016, 158: 116–143
https://doi.org/10.1016/j.engfracmech.2015.10.042
85 P Areias, T Rabczuk. Steiner-point free edge cutting of tetrahedral meshes with applications in fracture. Finite Elements in Analysis and Design, 2017, 132: 27–41
https://doi.org/10.1016/j.finel.2017.05.001
86 P Areias, J Reinoso, P P Camanho, J César de Sá, T Rabczuk. Effective 2D and 3D crack propagation with local mesh refinement and the screened Poisson equation. Engineering Fracture Mechanics, 2018, 189: 339–360
https://doi.org/10.1016/j.engfracmech.2017.11.017
87 C Anitescu, M N Hossain, T Rabczuk. Recovery-based error estimation and adaptivity using high-order splines over hierarchical T-meshes. Computer Methods in Applied Mechanics and Engineering, 2018, 328: 638–662
https://doi.org/10.1016/j.cma.2017.08.032
88 T Chau-Dinh, G Zi, P S Lee, T Rabczuk, J H Song. Phantom-node method for shell models with arbitrary cracks. Computers & Structures, 2012, 92–93: 242–256
https://doi.org/10.1016/j.compstruc.2011.10.021
89 P R Budarapu, R Gracie, S P Bordas, T Rabczuk. An adaptive multiscale method for quasi-static crack growth. Computational Mechanics, 2014, 53(6): 1129–1148
https://doi.org/10.1007/s00466-013-0952-6
90 H Talebi, M Silani, S P Bordas, P Kerfriden, T Rabczuk. A computational library for multiscale modeling of material failure. Computational Mechanics, 2014, 53(5): 1047–1071
https://doi.org/10.1007/s00466-013-0948-2
91 P R Budarapu, R Gracie, S W Yang, X Zhuang, T Rabczuk. Efficient coarse graining in multiscale modeling of fracture. Theoretical and Applied Fracture Mechanics, 2014, 69: 126–143
https://doi.org/10.1016/j.tafmec.2013.12.004
92 H Talebi, M Silani, T Rabczuk. Concurrent multiscale modeling of three dimensional crack and dislocation propagation. Advances in Engineering Software, 2015, 80: 82–92
https://doi.org/10.1016/j.advengsoft.2014.09.016
93 F Amiri, D Millán, Y Shen, T Rabczuk, M Arroyo. Phase-field modeling of fracture in linear thin shells. Theoretical and Applied Fracture Mechanics, 2014, 69: 102–109
https://doi.org/10.1016/j.tafmec.2013.12.002
94 P Areias, T Rabczuk, M Msekh. Phase-field analysis of finite-strain plates and shells including element subdivision. Computer Methods in Applied Mechanics and Engineering, 2016, 312: 322–350
https://doi.org/10.1016/j.cma.2016.01.020
95 H Ren, X Zhuang, Y Cai, T Rabczuk. Dual-horizon peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476
https://doi.org/10.1002/nme.5257
96 H Ren, X Zhuang, T Rabczuk. Dual-horizon peridynamics: A stable solution to varying horizons. Computer Methods in Applied Mechanics and Engineering, 2017, 318: 762–782
https://doi.org/10.1016/j.cma.2016.12.031
97 T Rabczuk, P Areias, T Belytschko. A meshfree thin shell method for non-linear dynamic fracture. International Journal for Numerical Methods in Engineering, 2007, 72(5): 524–548
https://doi.org/10.1002/nme.2013
98 T Rabczuk, T Belytschko. A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29–30): 2777–2799
https://doi.org/10.1016/j.cma.2006.06.020
99 T Rabczuk, R Gracie, J H Song, T Belytschko. Immersed particle method for fluid-structure interaction. International Journal for Numerical Methods in Engineering, 2010, 81: 48–71
100 T Rabczuk, S Bordas, G Zi. On three-dimensional modelling of crack growth using partition of unity methods. Computers & Structures, 2010, 88(23–24): 1391–1411
https://doi.org/10.1016/j.compstruc.2008.08.010
101 T Rabczuk, G Zi, S Bordas, H Nguyen-Xuan. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37–40): 2437–2455
https://doi.org/10.1016/j.cma.2010.03.031
102 T Rabczuk, T Belytschko. Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343
https://doi.org/10.1002/nme.1151
103 T Rabczuk, T Belytschko, S Xiao. Stable particle methods based on Lagrangian kernels. Computer Methods in Applied Mechanics and Engineering, 2004, 193(12–14): 1035–1063
https://doi.org/10.1016/j.cma.2003.12.005
104 F Amiri, C Anitescu, M Arroyo, S P A Bordas, T Rabczuk. XLME interpolants, a seamless bridge between XFEM and enriched meshless methods. Computational Mechanics, 2014, 53(1): 45–57
https://doi.org/10.1007/s00466-013-0891-2
105 T J Hughes, J A Cottrell, Y Bazilevs. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 2005, 194(39–41): 4135–4195
https://doi.org/10.1016/j.cma.2004.10.008
106 N Nguyen-Thanh, H Nguyen-Xuan, S P A Bordas, T Rabczuk. Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids. Computer Methods in Applied Mechanics and Engineering, 2011, 200(21–22): 1892–1908
https://doi.org/10.1016/j.cma.2011.01.018
107 V P Nguyen, C Anitescu, S P Bordas, T Rabczuk. Isogeometric analysis: An overview and computer implementation aspects. Mathematics and Computers in Simulation, 2015, 117: 89–116
https://doi.org/10.1016/j.matcom.2015.05.008
108 H Ghasemi, H S Park, T Rabczuk. A level-set based IGA formulation for topology optimization of flexoelectric materials. Computer Methods in Applied Mechanics and Engineering, 2017, 313: 239–258
https://doi.org/10.1016/j.cma.2016.09.029
109 N Nguyen-Thanh, J Kiendl, H Nguyen-Xuan, R Wüchner, K U Bletzinger, Y Bazilevs, T Rabczuk. Rotation free isogeometric thin shell analysis using PHT-splines. Computer Methods in Applied Mechanics and Engineering, 2011, 200(47–48): 3410–3424
https://doi.org/10.1016/j.cma.2011.08.014
110 N Nguyen-Thanh, N Valizadeh, M Nguyen, H Nguyen-Xuan, X Zhuang, P Areias, G Zi, Y Bazilevs, L De Lorenzis, T Rabczuk. An extended isogeometric thin shell analysis based on Kirchhoff-Love theory. Computer Methods in Applied Mechanics and Engineering, 2015, 284: 265–291
https://doi.org/10.1016/j.cma.2014.08.025
111 N Nguyen-Thanh, K Zhou, X Zhuang, P Areias, H Nguyen-Xuan, Y Bazilevs, T Rabczuk. Isogeometric analysis of large-deformation thin shells using RHT-splines for multiple-patch coupling. Computer Methods in Applied Mechanics and Engineering, 2017, 316: 1157–1178
https://doi.org/10.1016/j.cma.2016.12.002
112 N Vu-Bac, T Duong, T Lahmer, X Zhuang, R Sauer, H Park, T Rabczuk. A NURBS-based inverse analysis for reconstruction of nonlinear deformations of thin shell structures. Computer Methods in Applied Mechanics and Engineering, 2018, 331: 427–455
https://doi.org/10.1016/j.cma.2017.09.034
113 H Ghasemi, H S Park, T Rabczuk. A multi-material level set-based topology optimization of flexoelectric composites. Computer Methods in Applied Mechanics and Engineering, 2018, 332: 47–62
https://doi.org/10.1016/j.cma.2017.12.005
114 S S Ghorashi, N Valizadeh, S Mohammadi, T Rabczuk. T-spline based XIGA for fracture analysis of orthotropic media. Computers & Structures, 2015, 147: 138–146
https://doi.org/10.1016/j.compstruc.2014.09.017
115 S Kumari, R Vijay. Effect of symlet filter order on denoising of still images. Advances in Computers, 2012, 3(1): 137–143
https://doi.org/10.5121/acij.2012.3112
116 P J Rousseeuw, A M Leroy. Robust Regression & Outlier Detection. Hoboken: John Wiley & Sons, 1987
117 J Samadi. Seismic Behavior of Structure-equipment in a petrochemical complex to evaluate vulnerability assessment: A case study. Thesis for the Master’s Degree. Tehran: Civil Engineering, University of Tehran, 2010
118 A Jensen, A la Cour-Harbo. Ripples in Mathematics: The Discrete Wavelet Transform. Heidelberg: Springer Science & Business Media. 2001
119 K Soman. Insight into Wavelets: From Theory to Practice. New Delhi: PHI Learning Pvt. Ltd., 2010
120 M V Wickerhauser. Adapted Wavelet Analysis: From Theory to Software. Natick: AK Peters/CRC Press, 1996
121 D L Donoho, J M Johnstone. Ideal spatial adaptation by wavelet shrinkage. Biometrika, 1994, 81(3): 425–455
https://doi.org/10.1093/biomet/81.3.425
122 C M Stein. Estimation of the mean of a multivariate normal distribution. Annals of Statistics, 1981, 9(6): 1135–1151
https://doi.org/10.1214/aos/1176345632
123 H Yousefi, S S Ghorashi, T Rabczuk. Directly simulation of second order hyperbolic systems in second order form via the regularization concept. Communications in Computational Physics, 2016, 20(1): 86–135
https://doi.org/10.4208/cicp.101214.011015a
124 H Yousefi, A Noorzad, J Farjoodi. Multiresolution based adaptive schemes for second order hyperbolic PDEs in elastodynamic problems. Applied Mathematical Modelling, 2013, 37(12–13): 7095–7127
https://doi.org/10.1016/j.apm.2012.09.004
125 I W Selesnick, I Bayram. Total Variation Filtering, White paper, Connexions Web site. 2010
Related articles from Frontiers Journals
[1] Hassan YOUSEFI, Jamshid FARJOODI, Iradj MAHMOUDZADEH KANI. Adaptive simulation of wave propagation problems including dislocation sources and random media[J]. Front. Struct. Civ. Eng., 2019, 13(5): 1054-1081.
[2] Ivan Gomez ARAUJO, Esperanza MALDONADO, Gustavo Chio CHO. Ambient vibration testing and updating of the finite element model of a simply supported beam bridge[J]. Front Arch Civil Eng Chin, 2011, 5(3): 344-354.
[3] Zhigen WU, Guohua LIU, Zihua ZHANG. Experimental study of structural damage identification based on modal parameters and decay ratio of acceleration signals[J]. Front Arch Civil Eng Chin, 2011, 5(1): 112-120.
[4] ZHAO Mingjie, XU Xibin. Tomographic diagnosis of defects in hydraulic concrete structure[J]. Front. Struct. Civ. Eng., 2008, 2(3): 226-232.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed